Semi-automated heart valve morphometry and computational stress analysis from 3D images

ABSTRACT

A method is provided for measuring or estimating stress distributions on heart valve leaflets by obtaining three-dimensional images of the heart valve leaflets, segmenting the heart valve leaflets in the three-dimensional images by capturing locally varying thicknesses of the heart valve leaflets in three-dimensional image data to generate an image-derived patient-specific model of the heart valve leaflets, and applying the image-derived patient-specific model of the heart valve leaflets to a finite element analysis (FEA) algorithm to estimate stresses on the heart valve leaflets. The images of the heart valve leaflets may be obtained using real-time 3D transesophageal echocardiography (rt-3DTEE). Volumetric images of the mitral valve at mid-systole may be analyzed by user-initialized segmentation and 3D deformable modeling with continuous medial representation to obtain, a compact representation of shape. The regional leaflet stress distributions may be predicted in normal and diseased (regurgitant) mitral valves using the techniques of the invention.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. Ser. No. 16/355,231, filedMar. 15, 2019, which is a continuation of U.S. Ser. No. 15/697,169,filed Sep. 6, 2017 (now U.S. Pat. No. 10,235,754), which is acontinuation of U.S. Ser. No. 14/774,325, filed Sep. 10, 2015 (now U.S.Pat. No. 9,779,496), which is the U.S. National Stage of InternationalApplication No. PCT/US2014/024082, filed Mar. 12, 2014, which claims thebenefit of U.S. Provisional Application No. 61/788,691, filed Mar. 15,2013, the entire disclosures of each of which are incorporated herein byreference for any and all purposes.

TECHNICAL FIELD

The invention relates to methods of analyzing heart valves using 3Dimages of the heart valves and, more particularly, to techniques forsemi-automating the process of providing heart valve morphometry forcomputational stress analysis using 3D ultrasound.

BACKGROUND

Mitral valve (MV) disease is common in humans and not infrequentlyfatal. Mitral regurgitation, in particular, demonstrates astrongly-graded relationship between severity and reduced survival. MVsurgery, both repair and replacement, are commonly exercised treatmentoptions for mitral regurgitation. Imaging and assessment of the mitralvalve has traditionally been achieved by qualitative 2D ultrasound imageanalysis. Recently, real-time three-dimensional transesophagealechocardiography (rt-3DTEE) has become widely available and implemented.3D image-based modeling of the mitral valve is increasingly useful, andfinite element analysis (FEA) has been applied to the MV frequently overthe last 20 years.

To date, the majority of valve morphometry studies have employed manualtracing to reconstruct valve geometry from 3D echocardiographic imagedata. Therefore, the first objective herein is to introduce analternative semi-automated approach to valve morphometry based on asimple and rapid approach to user-initialized image segmentation thatexploits the contrast between the mitral valve tissue and surroundingblood pool in rt-3DTEE images. The valve is subsequently modeled using3D continuous medial representation to obtain localized thickness mapsof the mitral leaflets.

The inventors recently provided a framework for the application of invivo MV geometry and FEA to human MV physiology, pathophysiology, andrepair. (see, Xu C, Brinster C J, Jassar A S, et al. A novel approach toin vivo mitral valve stress analysis. Am J Physiol Heart Circ Physiol.299(6):1790-1794, 2010). Therefore, a second objective herein is todemonstrate that the semi-automated 3D MV model can be loaded withphysiologic pressures using FEA, yielding reasonable and meaningfulstress and strain magnitudes and distributions. Furthermore, theinventors endeavor to demonstrate this capability in both healthy anddiseased human mitral valves. The methods of the invention address theseand other objectives.

SUMMARY

Particular embodiments of the methods of the invention usehigh-resolution image-derived geometric models of the mitral valve asanatomically accurate input to finite element analysis (FEA) in order toestimate localized stress distributions on the mitral leaflets. A keyproperty of the models is that they volumetrically represent theleaflets (as structures with locally varying finite thickness). Allprevious studies have made very generic assumptions of leaflet thicknessin their FEA studies. For example, leaflet thickness was assumed to beuniform or have a generic, uniformly distributed thickness pattern.These assumptions have been based primarily on ex vivo analysis ofporcine valve tissue, rather than in vivo human valve tissue. A recentreview by Rausch et al. (“Mechanics of the Mitral Valve”, Biomech ModelMechanobiol. 2012) indicates that leaflet thickness is one of the mostinfluential parameters in biomechanical simulations of the mitral valve,which supports the relevance and significance of the volumetric modelsas described herein. The methods of the invention thus assess valvemorphology and thickness in vivo in order to measure or estimate thestresses on mitral valve leaflets to improve mitral valve repairdurability. As will be apparent to those skilled in the art from thefollowing description, the techniques described herein need not belimited to mitral valve leaflets but may also be applied to other heartvalve leaflets.

Exemplary embodiments of the method of the invention relate to measuringor estimating stress distributions on heart valve (e.g., mitral valve)leaflets to, for example, improve heart valve repair durability byobtaining three-dimensional images of the heart valve leaflets,segmenting the heart valve leaflets in the three-dimensional images bycapturing and/or quantifying locally varying thicknesses of the heartvalve leaflets in three-dimensional image data to generate animage-derived patient-specific model of the heart valve leaflets, andapplying the image-derived patient-specific model of the heart valveleaflets to a finite element analysis (FEA) algorithm to estimatestresses on the heart valve leaflets. The patient-specific model of theheart valve leaflets may be applied to the FEA algorithm usingimage-derived thickness measurements of the heart valve leaflets asinput material parameters. The images may be obtained by a number oftechniques including three-dimensional echocardiography.

Segmenting the heart valve leaflets may be performed manually, withactive contour evolution, with multi-atlas segmentation, or with adeformable modeling method. For example, user-initializedthree-dimensional active contour evolution based on region competitionmay be used to segment the heart valve leaflets in the three-dimensionalimage data. User-initialized regional of interest (ROI) extraction mayinclude construction of a two-dimensional maximum intensity projectionimage along an axial dimension of the image volume of the heart valveleaflet images and application of adaptive histogram equalization to theprojection image to enhance an annular rim and leaflet coaptation zoneof the heart valve. The user may outline the heart valve and mark aleaflet coaptation curve in the enhanced projection image, select athreshold for region competition, and use the resulting information toinitialize three-dimensional active contour segmentation. The level setmethod may be used to solve for the final three-dimensionalsegmentation.

The user-initialized segmentation method may be used to obtainthree-dimensional binary images of the anterior and posterior leafletsof the mitral valve, from which localized measurements of leafletthickness can be computed. To obtain localized leaflet thicknessmeasurements, the shape of each heart valve leaflet may be modeled withthree-dimensional continuous medial representation (cm-rep). Apatient-specific cm-rep of the heart valve leaflets may be obtained byfitting a deformable medial model (a cm-rep template of the heart valveleaflets) to binary segmentations of the heart valve leaflets byBayesian optimization. Each heart valve leaflet may be treated as aseparate shape, whose morphological skeleton comprises a single medialmanifold. The medial manifold and surface boundaries of the cm-rep ofeach heart valve leaflet may be discretely represented by a triangulatedmesh. Each node of the medial mesh may quantify a localized leafletthickness measurement, defined as the chord length or distance betweentwo boundary points associated with that node on medial mesh. DuringBayesian optimization, the mesh of each heart valve leaflet may bedeformed such that the similarity between the leaflet mesh and itscorresponding segmentation is maximized. For increased efficiency duringmodel fitting, a Laplace eigenfunction basis may be defined on themedial mesh such that the medial mesh is deformed smoothly by modifyingcoefficients of a small number of basis functions rather than allvertices of the mesh. Model fitting may be performed in stages withincreasing resolution to enhance model fitting accuracy and speed. In anexemplary embodiment, an atrial surface of the fitted cm-rep of eachmitral valve leaflet is applied to the FEA algorithm for finite elementanalysis, using locally defined leaflet thickness at each point on theatrial surface as input information.

BRIEF DESCRIPTION OF THE DRAWINGS

The various novel aspects of the invention will be apparent from thefollowing detailed description of the invention taken in conjunctionwith the accompanying drawings, of which:

FIGS. 1A-1E illustrate application of a semi-automated segmentationalgorithm in an exemplary embodiment.

FIGS. 2A-2C illustrate reconstructions of mid-systolic diseased (left)and normal (right) mitral valves from 3DE image data, including (2A) theresults of image segmentation, (2B) the fitted medial models, and (2C)the radial thickness field R mapped to the medial manifold of eachleaflet.

FIG. 3 illustrates a two-dimensional diagram of medial geometry.

FIGS. 4A-4D illustrate finite element models of mid-systolic diseased(4A-4C) and normal (4B, 4D) mitral valves reconstructed from rt-3DTEE,in transvalvular (4A, 4B) and oblique (4C, 4D) views.

FIG. 5 illustrates von Mises stress contour maps of diseased (left) andnormal (right) mitral valves.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The invention will be described in detail below with reference to FIGS.1A-5 . Those skilled in the art will appreciate that the descriptiongiven herein with respect to those figures is for exemplary purposesonly and is not intended in any way to limit the scope of the invention.All questions regarding the scope of the invention may be resolved byreferring to the appended claims. For example, though mitral valves arediscussed exclusively in the exemplary embodiment, it will beappreciated that the techniques described herein may be applied to otherheart valves as well.

Methods

Image Acquisition

Intra-operative rt-3DTEE data sets were obtained from two patients, onewith severe ischemic mitral regurgitation (IMR) and one without mitralvalve disease. The electrocardiographically gated images were acquiredwith an iE33 scanner (Philips Medical Systems, Andover, Mass.) using a 2to 7 MHz transesophageal matrix-array transducer over four consecutivecardiac cycles. The frame rate was 17 to 30 Hz with an imaging depth of14 to 17 cm. The image volumes were exported in Cartesian format(224×208×208 voxels), with an approximate isotropic resolution of 0.7mm. From each rt-3DTEE data series, an image volume delineating themitral valve at mid-systole (a single time point in the cardiac cycle)was selected for analysis.

Semi-Automated Image Analysis

User-Initialized Segmentation

Segmentation of the mitral leaflets in accordance with the inventivetechnique has two steps: user-initialized region of interest (ROI)extraction, and 3D active contour segmentation based on regioncompetition. User-initialized ROI extraction begins with construction ofa 2D maximum intensity projection image along the axial dimension of theimage volume. Adaptive histogram equalization is applied to theprojection image to enhance the annular rim and leaflet coaptation zoneof the mitral valve. In this enhanced projection image, a user outlinesthe valve and marks the leaflet coaptation curve in 2D. This informationis then used to initialize 3D segmentation. The user selects a softthreshold for region competition, and a level set method is used toperform the final segmentation. The segmentation process is illustratedin FIGS. 1A-1E, and the anterior and posterior leaflet segmentations ofthe normal and diseased subjects are illustrated in FIG. 2A.

FIGS. 1A-1E illustrate an application of a semi-automated segmentationalgorithm in an exemplary embodiment. In FIG. 1A, the user initializesan ROI in a long-axis cross-section of the 3DE image volume, identifyingthe valve along the axial dimension. In FIG. 1B, the user initializesannular points in a projection image depicting the valve from an atrialperspective. In FIG. 1C, the user shifts posterior annular points intothe coaptation zone, forming an outline of the anterior leaflet. In FIG.1D, the user initialization is used to automatically generate a 3D ROIcontaining the valve in the image volume. Finally, in FIG. 1E, a finalsegmentation of the valve is obtained by thresholding and 3D activecontour evolution. (LA=left atrium, LV=left ventricle, AL=anteriorleaflet, PL=posterior leaflet).

FIG. 2A-2C illustrate reconstructions of mid-systolic diseased (left)and normal (right) mitral valves from 3DE image data, including 2A theresults of image segmentation, 2B the fitted medial models, and 2C theradial thickness field R mapped to the medial manifold of each leaflet.Note that, by definition, the medial manifold does not extend to theleaflet boundary, as there is a distance R between the manifold andleaflet surface. (AL=anterior leaflet, PL=posterior leaflet).

Mitral Valve Geometric Modeling

Once 3D binary images of the anterior and posterior leaflets areobtained, the method of the invention is used to model the shape of eachmitral leaflet using 3D continuous medial representation (cm-rep). Thoseskilled in the art will appreciate that the images may be obtained usingother imaging methods besides echocardiography and that othersegmentation methods, such as multi-atlas segmentation, may also beapplied before the cm-rep model fitting step. Unlike a surfacerepresentation that describes an object's boundary geometry, medialrepresentation is a compact representation of shape. First introduced byBlum, a shape's medial axis is defined as the locus of centers ofmaximal inscribed balls (MIBs), where each ball is tangent to theobject's boundary at a minimum of two points. In three dimensions, amedial representation is a locus of tuples (m,R)∈

³×

⁺, where m is the medial manifold formed by the centers of the MIBs andR refers to the radii of the MIBs centered at those points or,equivalently, to the distance between the medial axis and objectsurface. For reference, a 2D diagram of medial representation ispresented in FIG. 3 . Medial representation is exploited herein for itsability to assess local variations in leaflet thickness, derived fromthe radial thickness field R.

FIG. 3 illustrates a two-dimensional diagram of medial geometry. Thecurve through m represents the medial surface (skeleton) m. Themaximally inscribed circle centered at the dot on m has radius R, withtwo spokes (arrows) pointing to two points, b⁺ and b⁻, on the objectboundaries (curves through b⁺ and b⁻). The vector ∇_(m)R lies in thetangent plane of m and points in the direction of greatest change in R.Thickness is measured herein as chord length, illustrated by the dottedline spanning the distance between b⁺ and b⁻.

In the cm-rep framework, geometric representations of the mitralleaflets are obtained by fitting a deformable medial model, alsoreferred to as a template, to its binary segmentation by Bayesianoptimization. Each leaflet is treated as a separate shape, so the valveis modeled as two separate cm-reps, where each leaflet is a simpleobject whose skeleton consists of a single medial manifold. The medialmanifold of each leaflet is represented by a mesh with 500 to 600 nodesand 900 to 1000 triangulated elements and is associated with atriangulated boundary mesh that represents the surface of the leaflet.Template fitting, or mesh deformation, consists of three stages: onealignment stage, one multi-resolution fitting stage, and a finaldeformation stage where both leaflets are simultaneously fitted to theleaflet segmentations. (1) During the first stage, Jenkinson's FLIRTaffine registration tool is used to obtain a similarity transform thataligns the leaflet templates with their corresponding segmentations. (2)The leaflet medial models are then independently deformed to fit thebinary leaflet segmentations at three different resolutions. Theobjective function minimized during deformation incorporates thevolumetric overlap error between the medial model and binarysegmentation, as well as regularization terms and inequality constraintsrequired by inverse skeletonization. (3) Finally, to correct for anyintersection of the leaflet models, the medial models of the twoleaflets are combined into a single model during the third stage offitting. During the simultaneous fitting of both leaflets, a leafletintersection penalty term is used to correct and prevent intersection ofthe leaflets' medial models. For increased efficiency during the lasttwo steps of template fitting, the Laplace eigenfunction basis isdefined on the medial template such that it can be deformed smoothly bymodifying the coefficients of a small number of basis functions ratherthan all vertices of the template mesh. The results of model fitting areshown in FIG. 2(b), and the radial thickness field R mapped to themedial manifold of each leaflet is shown in FIG. 2(c) for both thenormal and diseased valves.

In the methods described herein, the atrial surface of the fittedboundary mesh of each leaflet is used for finite element analysis. Ateach node of the mesh, localized leaflet thickness is quantified aschord length, i.e. the distance between the two boundary patches b⁺ andb⁻ associated with each point m on the medial manifold, as shown in FIG.3 .

Finite Element Analysis

To obtain high-quality meshes for complex shapes such as mitralleaflets, the atrial sides of the leaflet surfaces acquired fromsemi-automated image analysis were first imported into HyperMesh 10.0(Altair Inc.) as triangular elements, where raw nodal points were added,suppressed, or replaced to refine the leaflets' topological detailswithout changing geometrical shape. The mesh quality criteria includedelement Jacobian, element size, minimum and maximum angles, andskewness. The refined triangulated leaflet surfaces were modeled as thinshells (type S3R). The thickness measurements acquired from the rt-3DTEEdata were interpolated and assigned to each node in the refined leafletmesh using Matlab (the Mathworks, Natick, Mass.). Leaflet tissue wasassumed to be orthotropic and linearly elastic, with a Poisson's ratioof 0.49, and Young's modulus determined from excised porcine tissue data(Table 1). The coaptation area between the anterior and posteriorleaflet was defined as an interface pair with coefficient of frictionμ=0.3. Thirty-two chordae originating from each papillary muscle tipwere inserted symmetrically into the anterior and posterior leafletsalong the free edges of the leaflets (primary chordae), or moreperipherally (secondary chordae). Papillary muscle tips were modeled assingle points hinged in space associated with rotational freedom only.Chordae tendinae were represented by strings connecting the papillarymuscle tips to the insertion points on the leaflets, and modeled by atension-only truss element (type T3D2). Commercial FEA software(ABAQUS/Explicit 6.9, HKS Inc. Pawtucket, R.I.) was used to analyze thedeformation and resulting stress distribution in the mitral valvemodels, as previously described by the inventors in the afore-mentionedarticle. Systolic loading was accomplished via application of an 80 mmHgpressure gradient across the mitral valve. Stress, strain anddisplacement were recorded as output variables.

TABLE 1 Mitral valve material properties used in FEA model AnteriorPosterior Primary Secondary Parameter leaflet leaflet chordae chordaeCross-sectional — — 0.4  0.7  Area (mm²) E_(circumferential) (Pa) 6.20 ×10⁶ 2.35 × 10⁶ 4.20 × 10⁷ 2.20 × 10⁷ E_(radial) (Pa) 2.10 × 10⁶ 1.887 ×10⁶  — — Poisson's Ratio 0.49 0.49 0.49 0.49 Density (kg/m³) 1.04 × 10³1.04 × 10³ 1.04 × 10³ 1.04 × 10³Results

The mean and maximal AL and PL thicknesses derived from 3DE are reportedin Table 2, for both the normal and the diseased mitral valve. Theregurgitant orifice of the diseased valve was clearly imaged anddepicted in the 3D model, as demonstrated in FIGS. 4A-4D. FIGS. 4A-4Dillustrate finite element models of mid-systolic diseased 4A, 4C andnormal 4B, 4D mitral valves reconstructed from rt-3DTEE, intransvalvular 4A, 4B and oblique 4C, 4D views. (Nodes and elements havebeen reduced for visualization purposes.)

FIG. 5 illustrates von Mises stress contour maps of diseased (left) andnormal (right) mitral valves predicted by FEA. Note the persistentorifice between the anterior and posterior leaflets in the regurgitantvalve despite some conformational change (deformation) with pressureloading. The regurgitant orifice of the diseased valve is evident in theloaded valve, though some conformational change (deformation) hasoccurred. The peak and mean stresses in the bellies of the AL and PL'sof each valve were similar (Table 3). Note that for both mitral valves,the peak AL belly stress was larger than the peak PL belly stress, andthe mean AL stress was significantly larger than the mean PL stress(P<0.001 in both the normal and the diseased valve).

TABLE 2 Mitral valve leaflet thicknesses Nodes Mean Maximum in (mm) (mm)mesh Anterior leaflet (normal) 2.6 4.7 13735 Posterior leaflet (normal)2.3 4.8 9148 Anterior leaflet (diseased) 2.4 5.1 9235 Posterior leaflet(diseased) 2.4 4.2 4125

TABLE 3 von Mises stress Mean (kPa) P-value Peak (kPa) Anterior leafletbelly (normal) 97.1 ± 37.2 215.5 Posterior leaflet belly (normal) 37.6 ±14.4 <.001 85.5 Anterior leaflet belly (diseased) 81.7 ± 19.2 192.8Posterior leaflet belly (diseased) 39.2 ± 16.3 <.001 134.8

DISCUSSION

A semi-automated and integrated methodology for imaging, segmenting,modeling, and deriving computationally-predicted pressure-derived mitralvalve leaflet stresses is presented herein, and points the way towardsintraoperative and periprocedural guidance from morphometric and stressmodeling of the mitral valve.

The methods described herein provide an approach to valve morphometrythat provides a comprehensive, automated assessment of 3D valvegeometry—in both normal and diseased mitral valves—by ultrasound imageanalysis. This is accomplished using an efficient segmentation strategythat exploits the contrast in 3D transesophageal images and usesprojections of 3D data to eliminate the need for the user to navigate a3D image volume during initialization. Though not emphasized herein, theincorporation of deformable registration with cm-rep allows for acompact parametric representation of valve shape, from which a number ofclinically significant features can be automatically derived. Inaddition, with the ability to establish points of correspondence onvalves of different subjects and on the same valve at different timepoints, deformable modeling with cm-rep lays the foundation forstatistical studies of time-dependent valve morphology.

A further advantage of the image analysis and segmentation algorithmsdescribed is that an objective measure of local mitral leaflet thicknessis provided. While these measurements have not been validated in vivo,the inventors are in the process of doing so. Ex vivo human mitral valveleaflet thicknesses have been described, and the image-derivedthicknesses are generally consistent with those pathologic measurementsand with prior echocardiographic measures of leaflet thicknesses innormal human mitral valves. The present invention presents the first FEAsimulation of the mitral valve incorporating high resolution in vivomeasurements of leaflet thickness.

The ability to reliably estimate patient-specific mitral leaflet andchordal stresses in vivo has important clinical implications. Repairfailure as manifest by the development of recurrent mitral regurgitationhas recently been demonstrated to be far more common than originallybelieved. Recent studies have also shown that repair failures oftenresult from stress related phenomenon such as chordal rupture, leafletsuture line disruptions and annuloplasty ring dehiscence. The ability toassess leaflet and chordal stresses in repaired valves will, withclinical experience, likely lead to improved surgical results byidentifying patients with high stress valves in the early post-operativeperiod. Such patients could either have re-repair or valve replacementbefore ever leaving the operating room, or could be subjected to closerpost-operative clinical follow-up.

There are some evident limitations of the methods described herein.First, the stress maps derived have not been tested against in vivoexperimental results. However, this deficit is characteristic of allprior work on the stress and strain behavior of the mitral valveapparatus: it is difficult or impossible to measure in vivo strains ofheart valves except in discrete matrices of transducers or markers.Second, the FEA utilizes a less-than-comprehensive mitral valve model:whereas the leaflet surface profile and papillary muscle tips areaccurately determined by rt-3DTEE, the chordae tendinae were notreliably imaged and so their incorporation in the model is, at best,heuristically motivated. This solution is admittedly suboptimal, butsimilar to that adopted in prior noninvasive mitral valve FEA studies(Votta, et al. 2008, “Mitral valve finite-element modeling fromultrasound data: a pilot study for a new approach to understand mitralfunction and clinical scenarios,” Philosophical transactions Series A,Mathematical, physical, and engineering sciences, 366, pp. 3411-3434).Prot et. al. used ex vivo examination of porcine valves to determine thenumber and insertions of secondary chordae (Prot et al., “Finite elementanalysis of the mitral apparatus: annulus shape effect and chordal forcedistribution,” Biomechanics and Modeling in Mechanobiology, Vol. 8, pp.43-55), but this approach is clearly impossible in most human studies.In addition, the material properties model (linearly elastic) used isrelatively simplified; however, the closed mitral valve has been shownto have a linear stress-strain relationship over the physiologic rangeof pressures. Finally, homogeneous and uniform material properties wereused in implementing the methods described herein. It is reasonable topresume that leaflet material properties will be different in diseasedand healthy mitral valves, and may vary regionally in a single valve.Nevertheless, the current research emphasizes the dependence ofmechanical stress on geometric derangements in the diseased mitralvalve.

Recently, the inventors have demonstrated that FEA modeling of the invivo human mitral valve using high-resolution 3D imaging is reasonableand useful for stress prediction in mitral valve pathologies and repairs(Xu). The methods described herein extend and amplify those results, andpromises near-real-time stress analysis in the human mitral valve usingautomated 3DE image analysis and modeling, and FEA. Therefore, arational approach to in vivo mitral valve stress analysis incorporatesrealistic empiric material properties of leaflets and chordae, 3Dimaging, semi-automated valve segmentation and modeling, and FEA.

Those skilled in the art will also appreciate that the invention may beapplied to other applications and may be modified without departing fromthe scope of the invention. For example, the techniques described hereinare not limited to measurement of mitral valve morphometry but also maybe applied to other heart valves as well. Also, the methods of theinvention may be applied to images obtained using other imaging methodsbesides echocardiography that permit quantification of the thickness ofthe heart valves. In addition, other segmentation methods, such asmanual tracing or multi-atlas segmentation, may also be applied beforethe cm-rep model fitting. Another possibility is to fit the cm-rep modeldirectly to the three-dimensional grayscale image. Accordingly, thescope of the invention is not intended to be limited to the exemplaryembodiments described above, but only by the appended claims.

What is claimed:
 1. A method of measuring or estimating stressdistributions on heart valve chordae tendinae in a subject, comprising:obtaining three-dimensional images of the heart valve leaflets;segmenting the heart valve leaflets in the three-dimensional images, inorder to obtain three-dimensional binary images of the heart valveleaflets from which localized measurements of leaflet thickness can becomputed; obtaining localized measurements of leaflet thickness bymodeling a shape of each heart valve leaflet with three-dimensionalmedial axis representation, in order to generate an image-derivedpatient-specific model of the heart valve leaflets; obtaining apatient-specific cm-rep of the heart valve leaflets by fitting adeformable medial model to binary segmentations of the heart valveleaflets by Bayesian optimization, and applying the image-derivedpatient-specific model of the heart valve leaflets to a finite elementanalysis (FEA) algorithm to estimate stresses on the heart valve chordaetendinae, wherein each heart valve leaflet is treated as a separateshape whose morphological skeleton comprises a single medial manifold;wherein the medial manifold and surface boundaries of the cm-rep of eachheart valve leaflet is discretely represented by a triangulated mesh andeach node of the mesh quantifies a localized leaflet thicknessmeasurement defined as a chord length or distance between two boundarypoints associated with that node on the mesh, wherein during theBayesian optimization the mesh of each heart valve leaflet is deformedsuch that a similarity between the mesh and its correspondingsegmentation is maximized, wherein a Laplace eigenfunction basis isdefined on the mesh during fitting of the deformable medial model suchthat the mesh is deformed smoothly by modifying coefficients of a smallnumber of basis functions rather than all vertices of the mesh, andwherein the fitting of the deformable medial model is performed instages with increasing resolution.
 2. The method of claim 1, wherein theobtaining step comprises imaging the heart valve leaflets usingechocardiography to obtain three-dimensional ultrasound images.
 3. Themethod of claim 1, wherein segmenting the heart valve leaflets isperformed manually with active contour evolution, with multi-atlassegmentation, or with a deformable modeling method.
 4. The method ofclaim 3, wherein the heart valve leaflets are segmented in thethree-dimensional image data by user-initialized three-dimensionalactive contour evolution based on region competition.
 5. The method ofclaim 4, wherein segmenting the heart valve leaflets further comprisesuser-initialized region of interest (ROI) extraction includingconstruction of a two-dimensional maximum intensity projection imagealong an axial dimension of an image volume of the heart valve leafletimages and application of adaptive histogram equalization to theprojection image to enhance an annular rim and leaflet coaptation zoneof the heart valve.
 6. The method of claim 5, wherein segmenting theheart valve leaflets further comprises a user outlining the heart valveand marking a leaflet coaptation curve in the enhanced projection image,selecting a threshold for region competition, and using resultinginformation to initialize said three-dimensional active contourevolution.
 7. The method of claim 6, wherein segmenting the heart valveleaflets further comprises using a level set method to solve for a finalthree-dimensional segmentation.
 8. The method of claim 1, wherein anatrial surface of the fitted cm-rep of each heart valve leaflet isapplied to the FEA algorithm for finite element analysis using locallydefined leaflet thickness at each point on the atrial surface as input.9. The method of claim 1, wherein the segmenting step includesquantifying locally varying thicknesses of the heart valve leaflets inthe three-dimensional image data.
 10. The method of claim 9, whereinquantifying locally varying thicknesses of the heart valve leaflets inthe three-dimensional image data comprises applying a deformable medialmodel that derives locally varying heart valve leaflet thicknessmeasurements from a medial axis representation of the heart valveleaflets.
 11. The method of claim 10, wherein the patient-specific modelof the heart valve leaflets is applied to said FEA algorithm usingimage-derived thickness measurements of the heart valve leaflets asinput material parameters.
 12. The method of claim 1, wherein the heartvalve is the mitral valve.